A model of mesoscopic plasticity was developed for studying initial-boundary value problems in small-scale plasticity. Qualitative finite-element based computational predictions of the theory were considered. Size effects and the development of marked inhomogeneity in the simple shearing of plastically constrained grains were demonstrated. A non-locality in elastic straining, leading to a strong Bauschinger effect, was analyzed. Low shear-strain boundary-layers in constrained simple shearing of infinite layers of polycrystalline materials were not predicted by the model. This result was justified on the basis of an examination of the no dislocation-flow boundary condition. The time-dependent spatially homogeneous simple shearing solution was studied numerically. The computational results, and an analysis of a continuous dependence with respect to the initial data of solutions for a model linear problem, revealed the need for a non-linear study of a stability transition of the homogeneous solution with decreasing grain size and increasing applied deformation. The continuous-dependence analysis also indicated a possible mechanism for the development of spatial inhomogeneity in the initial stages of deformation in lower-order gradient plasticity theory. The results of the thermal cycling of small-scale beams/films with various degrees of constraint to plastic flow were presented. These revealed size effects and reciprocal film-thickness scaling of the dislocation-density boundary-layer width.

Size Effects and Idealized Dislocation Microstructure at Small Scales - Predictions of a Phenomenological Model of Mesoscopic Field Dislocation Mechanics – II. A.Roy, A.Acharya: Journal of the Mechanics and Physics of Solids, 2006, 54[8], 1711-43